An Almost Tight RMR Lower Bound for Abortable Test-And-Set

TL;DR

This paper establishes a near-tight lower bound on the remote memory reference complexity for abortable test-and-set operations, highlighting a fundamental complexity gap from non-abortable variants in shared memory models.

Contribution

It proves a new lower bound for abortable test-and-set, demonstrating a separation from the constant complexity of non-abortable versions, and discusses implications for abortable implementations.

Findings

Omega(log n/loglog n) RMR lower bound for abortable test-and-set

Separation between abortable and non-abortable RMR complexities

Modification of existing implementations to achieve abortability

Abstract

We prove a lower bound of Omega(log n/loglog n) for the remote memory reference (RMR) complexity of abortable test-and-set (leader election) in the cache-coherent (CC) and the distributed shared memory (DSM) model. This separates the complexities of abortable and non-abortable test-and-set, as the latter has constant RMR complexity (Golab, Hendler, Woelfel, SIAM Journal of Computing Vol. 39, 2010). Golab, Hendler, Hadzilacos and Woelfel (Distributed Computing Vol. 25, 2012) showed that compare-and-swap can be implemented from registers and TAS objects with constant RMR complexity. We observe that a small modification to that implementation is abortable, provided that the used TAS objects are abortable.